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For a stratified pseudomanifold X, we have the de Rham Theorem H p (X) = H ∗ (X), for a perversity p verifying 0 ≤ p ≤ t, where t denotes the top perversity. We extend this result to any perversity p. In the direction cohomology 7→ homology, we obtain the isomorphism H ∗ p (X) = H t−p ∗ ( X,Xp ) , where Xp = ⋃

de Rham intersection cohomology for general perversities